Lie Symmetry Analysis of Fourth Order Nonlinear Harmonic Differential Equation.
2019
Khaguli, Adenyah, R.
Lie group theory is a very practical and handy mathematical approach and it can be used to obtain solutions to diverse problems in applied mathematics. It's rich, very interesting and in broad sense a topic of active mathematical research. Efforts to obtain solutions to a variety of differential equations by use of Lie symmetry have been in existence for a long period of time. The numerical methods applied in obtaining solutions provide approximations which depend on certain initial and boundary conditions. This in itself is a limitation which can be dealt with by obtaining an analytical solution. Lie symmetry analysis approach to solve a fourth order wave equation which mises in studying the group properties of the linear wave equation in an inhomogeneous medium has been clone. In this study we solved a harmonic fourth order non-linear ordinary differential equation using Lie Symmetry Group Invariant method. The methodology applied involved the use of infinitesimal generators, extended transformations, variation symmetries, adjoint-symmetries, integrating factors and the invariant transformations. This study obtained an analytic method for solving the harmonic fourth order non• linear equation. The result is of great significance in the field of mechanics.
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